郭柏靈論文集第十三卷收集的是郭柏靈先生發表于2014,2015年度的主要科研論文，涉及的方程范圍很廣，有確定性偏微分方程和隨機偏微分方程，研究的問題包括適定性、爆破性、漸近性等等。這些論文具有很高的學術價值，對偏微分方程、數學物理、非線性分析、計算數學等方向的科研工作者和研究生，是極好地參考著作。
Contents
2014年
H2-regularity Random Attractors of Stochastic Non-Newtonian Fluids with Multiplicative Noise .1
Global Existence of Smooth Solutions to the Model Equations for Turbulent Flows 17
Global Random Attractors for the Stochastic Dissipative Zakharov Equations 35
Global Smooth Solutions of the Generalized KS-CGL Equations for Flames Governed by a Sequential Reaction 57
Blow-up of Smooth Solutions to the Isentropic Compressible MHD Equations 80
Random Attractors of Stochastic Non-Newtonian Fluids on Unbounded Domain 90
Long Time Behavior of Solutions to Coupled Burgers-Complex Ginzburg-Landau (Burgers-CGL) Equations for Flames Governed by Sequential Reaction 103
High-order Rogue Waves in a Vector Nonlinear Schr.odinger Equations 129
Schr.odinger Limit of Weakly Dissipative Stochastic Klein-Gordon-Schr.odinger Equations and Large Deviations 142
Global Well-posedness for the Fractional Schr.odinger-Boussinesq System 172
The Stability of Stochastic Generalized Porous Media Equations with General Levy Noise 187
The Exponential Decay of Solutions and Traveling Wave Solutions for a Modiled Camassa-Holm Equation with Cubic Nonlinearity 204
Global Smooth Solutions for the Zakharov System with Quantum E.ects in Two Space Dimensions 227
Ergodicity of the Stochastic Fractional Reaction-Di.usion Equation 251
Existence of Generalized Heteroclinic Solutions of the Coupled Schr.odinger System under a Small Perturbation 288
On the Equations of Thermally Radiative Magnetohydrody namics 308
大氣、海洋動力學中一些非線性偏微分方程的研究 359
連串反應中控制火焰的耦合 GKS-CGL 方程組解的極限行為 376
2015 年
A Class of Stable and Conservative Finite Di.erence Schemes for the Cahn-Hilliard Equation 403
Di.usion Limit of 3D Primitive Equations of the Large-scale Ocean under Fast Oscillating Random Force 425
Existence of Topological Vortices in an Abelian Chern-Simons Model 446
Radiative Transfer in Two Adjoining Media: The Continuity of Thermal Flux and the Existence and Uniqueness of Solutions 461
Darboux Transformation and Multi-dark Soliton for N-component Nonlinear Schr.odinger Equations 505
The Cauchy Problem of the Modiled CH and DP Equations 528
Stochastic Korteweg-de Vries Equation Driven by Fractional Brownian Motion 556
Global Strong Spherically Symmetric Solutions to the Full Compressible Navier-Stokes Equations with Stress Free Boundary 580
Solutions of Ginzburg-Landau Theory for Atomic Fermi Gases near the BCS-BEC Crossover 613
Orbital Instability of Standing Waves for the Generalized 3D Nonlocal Nonlinear Schr.odinger Equations 628
Existence of the Global Smooth Solution to a Fractional Nonlinear Schr.odinger System in Atomic Bose-Einstein Condensates 661
Di.usion Limit of 3D Primitive Equations of the Large-scale Ocean under Fast Oscillating Random Force 680
Uniqueness of Weak Solutions to the 3D Ginzburg-Landau Superconductivity Model 701
High-Order Soliton Solution of Landau-Lifshitz Equation 709
Random Attractor and Stationary Measure for Stochastic Long-short Wave Equations 744
Global Well-Posedness of Stochastic Burgers Systerm 766
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